An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Fractals everywhere
Introduction to Solid Modeling
Introduction to Solid Modeling
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
A New Paradigm for Changing Topology during Subdivision Modeling
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
Guaranteeing 2-Manifold Property for Meshes
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Winged edge polyhedron representation.
Winged edge polyhedron representation.
A minimal and complete set of operators for the development of robust manifold mesh modelers
Graphical Models - Special issue on SMI 2002
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Insight for practical subdivision modeling with discrete gauss-bonnet theorem
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Interactive face-replacements for modeling detailed shapes
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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In this paper, we present a subdivision-inspired scheme to construct generalized Sierpinski polyhedron. Unlike usual Sierpinski polyhedra construction schemes, which create either an infinite set of disconnected tetrahedra or a non-manifold polyhedron, our robust construction scheme creates one connected and manifold polyhedron. Moreover, unlike the original schemes, this new scheme can be applied to any manifold polyhedral mesh and based on the shape of this initial polyhedra a large variety of Sierpinski polyhedra can be obtained. Our basic scheme can be viewed as applying simplest subdivision scheme [23] to an input polyhedron, but retaining old vertices. The porous structure is then obtained by removing the refined facets of the simplest subdivision.